What are the differences between renderman and cycles? How can I learn renderman?
Is Renderman better than Cycles?

YES and NO, it handles caustics better, has more options for your lights (light linking), Has had options for years that Cycles is just starting to get. Now the reason I rarely use RM21 is a couple things. 1. Only can use CPU, and they dont have any plans of making it work with GPU (Major Downside). You need another pop up window called "IT" to see your renders. I actually like this because it is so easy to do many render passes with just a click of the button, however it is not the ideal set up to see your quick renders within Blender. Sometimes I just want to switch into render view in Blender to quickly check something. This is not so easy to do with "IT".

Are renderman's nodes easier and faster than cycles'?

NO, roughly the same. There are some exceptions though. 

I saw this thing about Pixar's new Surface Shader that was used for Finding Dory and other PIXAR movies.

Blender practically has this now  with 2.79 called the Princepled Shader. 

My question is, what is the best way to learn shading and lighting for Renderman INSIDE blender?

https://renderman.pixar.com/forum/forumdisplay.php?s=&amp;forumid=166

Also, these questions are better to ask here:

https://blenderartists.org/forum/